The topic of this thesis is the Ethereum incentive mechanism, in particular the changes introduced in EIP-1559. The aim of the thesis is to investigate the behaviour and propose any potential improvements in case of discovered flaws. The previously used first price auction mechanism required users to choose the incentive arbitrarily, which led to overpaying and high fee volatility. These problems occurred mainly due to higher network utilization after the popularization of projects such as decentralized finance, NFT collections, and the metaverse. The new incentive mechanism introduced the variable block size, which can adapt to the current network usage. Base fee, a value that indicates the minimum fee needed to include the transaction in the block, is then calculated based on the utilization of the previous block, making the fees more predictable. Several simulation experiments were proposed to investigate the typical behaviour and possible weaknesses of the mechanism. Finally, a possible improvement was found, and future research was proposed. The goals of the thesis were achieved, and the results were presented in the thesis.